Two blocks of masses 2 kg and 4 kg are connected through a massless inextensible string. The co-efficient of friction between 2 kg block and ground is 0.4 and the coefficient of friction between 4 kg block and ground is 0.6. Two forces F1 = 10 N and F2 = 20 N are applied on the blocks . Calculate the frictional force between 4 kg block and ground (Assume initially the tension in the string was just zero before forces F1 and F2 were applied)

To solve this problem, we need to analyze the forces acting on both blocks and determine the frictional force acting on the 4 kg block. Let's break it down step by step.

Understanding the Forces Involved

We have two blocks connected by a string, with different masses and coefficients of friction. The forces applied to each block are:

• F1 = 10 N on the 2 kg block
• F2 = 20 N on the 4 kg block

Calculating the Maximum Frictional Forces

The frictional force can be calculated using the formula:

Frictional Force (f) = μ * N

where μ is the coefficient of friction and N is the normal force. For both blocks, the normal force is equal to their weight since they are on a horizontal surface.

For the 2 kg Block

The normal force (N1) for the 2 kg block is:

N1 = m1 * g = 2 kg * 9.81 m/s² = 19.62 N

The maximum frictional force (f1) is:

f1 = μ1 * N1 = 0.4 * 19.62 N = 7.848 N

For the 4 kg Block

The normal force (N2) for the 4 kg block is:

N2 = m2 * g = 4 kg * 9.81 m/s² = 39.24 N

The maximum frictional force (f2) is:

f2 = μ2 * N2 = 0.6 * 39.24 N = 23.544 N

Net Forces Acting on Each Block

Next, we need to determine the net forces acting on each block. The tension in the string will affect the forces acting on the 2 kg block, but since we assume the tension is initially zero, we can analyze the forces directly.

For the 2 kg Block

The net force (F_net1) acting on the 2 kg block is:

F_net1 = F1 - f1 = 10 N - 7.848 N = 2.152 N

For the 4 kg Block

The net force (F_net2) acting on the 4 kg block is:

F_net2 = F2 - f2 = 20 N - 23.544 N = -3.544 N

A negative net force indicates that the frictional force is greater than the applied force, meaning the block does not move. Therefore, the frictional force must equal the applied force.

Determining the Frictional Force on the 4 kg Block

Since the 4 kg block is not moving, the frictional force (f2) must equal the applied force (F2) to prevent motion:

f2 = F2 = 20 N

Final Result

Thus, the frictional force acting on the 4 kg block is:

Frictional Force = 20 N

In summary, even though the maximum frictional force calculated was 23.544 N, the actual frictional force acting on the 4 kg block is limited by the applied force of 20 N, as the block does not move. This illustrates how friction adjusts to balance the forces in a static situation.